Question

Use the provided information to write the standard form equation of the parabola.

Answer 1

Answer:

           f(x) = x² - 6x + 3

Step-by-step explanation:

Parabola f(x) = ax² + bx + c passing through point (x₁, y₁) means if x=x₁ then f(x)=f(x₁)=y₁

(0, 3) ⇒  3=a·0²+b·0+c    ⇒   c=3

f(x) = ax² + bx + 3

(4, -5)  ⇒  -5 = a·4² + b·4 + 3  

               -5 =  16a + 4b + 3

              -4b = 16a + 8

               b = - 4a - 2

(-1, 10)  ⇒  10 = a·(-1)² + b·(-1) + 3

                10 = a - b + 3

                 b = a - 7

a - 7 = - 4a - 2

5a = 5

a = 1

b = 1 - 7 = - 6

So the equation:

                         f(x) = x² - 6x + 3